Математика15 мин

Ratio and Proportion

Split quantities by ratio, scale recipes, and recognise direct vs inverse proportion in disguise.

Ratios and parts

A ratio $a:b$ tells you how a whole is divided into parts. To split a total $T$ in ratio $a:b$ , give one share $\dfrac{a}{a+b}\,T$ and the other $\dfrac{b}{a+b}\,T$ .

Splitting money

Split $4500 in the ratio 4:5.

Total parts: $4 + 5 = 9$ .
Each part: $4500 / 9 = 500$ .
Shares: $4 \times 500 = 2000$ and $5 \times 500 = 2500$ .

Жауап: $2000 and$ 2500

Direct and inverse proportion

Read the story: more workers → less time = inverse. More litres → more cost = direct.

Жаттығу

If 6 workers paint a wall in 8 hours, how long for 4 workers?

Жауап пен түсініктемені көру

Жауап: 12 hours

Inverse: workers × hours = constant. $6 \cdot 8 = 48$ , so $48 / 4 = 12$ .

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